We study m-closed cellular algebras (coherent connguration) and m-isomorphisms of cellular algebras which can be regarded as mth approximations to Schurian algebras (i.e. the centralizer algebras of permutation groups) and to strong isomorphisms (i.e. bijections of the point sets taking one algebra to the other) respectively. If m = 1 we come to arbitrary cellular algebras and their weak isomor...

We define and study m-closed cellular algebras (coherent configurations) and m-isomorphisms of cellular algebras which can be regarded as mth approximations of Schurian algebras (i.e. the centralizer algebras of permutation groups) and of strong isomorphisms (i.e. bijections of the point sets taking one algebra to the other) respectively. If m = 1 we come to arbitrary cellular algebras and thei...

The notion of isomorphisms of types has many theoretical as well as practical consequences, and isomorphisms of types have been investigated at length over the past years. Isomorphisms in weak system (like linear lambda calculus) have recently been investigated due to their practical interest in library search. In this paper we give a remarkably simple and elegant characterization of linear iso...

Weisfeiler on the occasion of the 30th anniversary of their paper where the cellular algebra rst appeared. Abstract We deene and study m-closed cellular algebras (coherent conngurations) and m-isomorphisms of cellular algebras which can be regarded as mth approximations of Schurian algebras (i.e. the centralizer algebras of permutation groups) and of strong isomorphisms (i.e. bijections of the ...

The notion of isomorphisms of types has many theoretical as well as practical consequences, and isomorphisms of types have been investigated at length over the past years. Isomorphisms in weak system (like linear lambda calculus) have recently been investigated due to their practical interest in library search. In this paper we give a remarkably simple and elegant characterization of linear iso...

We observe that for planar graphs, the geometric duality relation generates both 2-isomorphism and abstract duality. This observation has surprising consequence links, equivalence defined by isomorphisms of checkerboard graphs is same as 2-isomorphisms graphs.

We prove induced Ramsey theorems in which the monochromatic induced subgraph satisfies that all members of a prescribed set of its partial isomorphisms extend to automorphisms of the colored graph (without requirement of preservation of colors). We consider vertex and edge colorings, and extensions of partial isomorphisms in the set of all partial isomorphisms between singletons as considered b...

Homotopy theory studies topological spaces up to homotopy, so it must study the functor π∗ : Top → Π−algebras. Passage to the homotopy category is declaring π∗-isomorphisms to be isomorphisms. Because this functor is difficult to compute, one way to do homotopy theory is to study simpler functors which also map to graded abelian categories, e.g. πQ ∗ , H∗(−;Z), K∗, or more generally E∗ for E so...

The characterization of second-order type isomorphisms is a purely syntactical problem that we propose to study under the enlightenment of game semantics. We study this question in the case of second-order λμ-calculus, which can be seen as an extension of system F to classical logic, and for which we define a categorical framework: control hyperdoctrines. Our game model of λμ-calculus is based ...